computer logic & logic gates justin champion. iitct contents introduction to logic look at the...
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Computer Logic & Logic Gates
Justin Champion
IITCT
ContentsIntroduction to LogicLook at the different Logic GatesSummary
IITCT - Logic
George Boole 1815 to 1864
Boole approached logic in a new way reducing it to a simple algebra, incorporating logic into mathematics. He also worked on differential equations, the calculus of finite differences and general methods in probability.
IITCT - Logic Boolean Logic
Something is either• True or False• 1 or 0• Correct or Wrong
Computers use this to make decisions• A computer is basically a large number of switches
• Each of these can be either in the state of on (1) or off (0)
We do use this kind of logic every single day
IITCT
You can only get into the night club if you have a coloured suit
TrueGet into Club
FalseRefused Entry to Club
IITCT Logic
As seen you use this all the time• If (suit coloured) then
• Entry to club
• Else• Refused Entry
You can also put multiple conditions together Conditional Logic
• If (Suit Coloured and hat on the head) then• Entry to club
• Else• Refused Entry
IITCT You can only get into the club if you have a coloured suit
and a hat on your head!
FalseRefused
TrueAccepted
FalseRefused
FalseRefused
IITCT All of the previous are examples of Boolean Logic
Basic Logic Conditions Available• AND• OR• NOT
Logic Symbols used in diagrams• AND .• OR +• NOT
IITCT Use of The Logic Symbols
If person wearing a Jacket AND a tie then enter Entry = Jacket.Tie
If person wearing a jacket which is NOT white AND a tie then enter
Entry = (jacket.white).tie
IITCT What you have seen is every day examples of Logic
This is exactly what is used inside of computers to make decisions
The following section will look at the formal method describing truth tables• This is no more complicated than the previous examples• It is just a matter of realising this fact
IITCT Switches
To represent the logic of 1 and 0 we use switches which turn off (0) and on (1)
These switches are referred to as transistors
Emitter
Collector
Base
0 Volts
No Flow
Emitter
Collector
Base
1 Volt
Flow
IITCT Processors use large numbers of these transistors to
make decisions AMD 3200+ processor has 54.3 Million transistors!
IITCT Example Truth Tables
A B A.B A+B A A+B
0 0 0 0 1 1
0 1 0 1 1 0
1 1 1 1 0 0
1 0 0 1 0 0AND OR NOT NOT (A or B)
IITCT To create a truth table first of all list all of the conditions
For binary values the number of unique conditions will be• 2 number of conditions
• So for this example it will 22 giving 4 unique conditions• For 3 conditions it will be 23 giving 8 unique conditions
A B
0 0
0 1
1 1
1 0
IITCT Try a truth table yourself
Create a truth table for• If man has long hair and not a member entry refused
IITCT Answer
Create a truth table for• If person has long hair and not a member entry refused
Long Hair Member Not Member Long Hair.Member
0 1 0 Accepted
0 0 1 Accepted
1 1 0 Accepted
1 0 1 Refused
IITCT What this logic looks like in electrical circuits
First the truth table
A B X
0 0 0
0 1 0
1 0 0
1 1 1
IITCT What this logic looks like in electrical circuits
X = A.B A = 0, B = 0, X=0 Light is off
AND Gate
IITCT What this logic looks like in electrical circuits
X = A.B A = 1, B = 1, X=1 Light is on
AND Gate
IITCT The logic used can also be drawn out on a diagram
IITCT
And Gate - X = A.B
IITCT
Alarm System A = Alarm Set B = Door Sensor Opened X = Alarm Sounding
A B X (A.B)
0 0 0
0 1 1
1 0 1
1 1 1
IITCT
OR Example X = A + B
Alarm SetA = Window OpenedB = IR Sensor Detects movementX = Alarm Sounding
A B X
0 0 0
0 1 1
1 0 1
1 1 1
IITCT
The Boolean logic gates we have discussed are NOT exhaustive There are a lot more gates which can be used with
increasing complexity Example
• XOR• XAND
Later on in the course these logic gates will be used to carry out mathematical functions
IITCT
Why we learn this Boolean logic is used in electronics and computers to
carry out actions Programming Languages use this logic to test conditions It is the basis of all computing
IITCT Summary of what we have discussed
Boolean Logic